Subgroups — C₈×SD₁₆×D₆₁ #29649372

Order 15616.

822 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×SD₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#21444622	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#11758190	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×#92418	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#11758201	C₂	1	1	yes	maximal, characteristic, complemented
8	#21444618	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11758200	C₂	1	1	yes	maximal, characteristic, complemented
10	#21444616	C₂	1	1	yes	maximal, characteristic, complemented
11	#334×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈⋊C₈×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄⋊C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
14	C₈²×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×SD₁₆×D₆₁	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₆₁	—	2	1	no	—
18	C₄×Q₈×D₆₁	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₆₁	C₂²	1	1	yes	characteristic
20	Q₈×#92418	C₂²	1	1	yes	characteristic, complemented
21	C₈×Dic₁₂₂	—	2	1	no	—
22	C₈×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
23	#16839886	—	2	1	no	—
24	#16839886	C₂²	1	1	yes	characteristic, complemented
25	#16839853	C₄	1	1	yes	characteristic
26	C₄×#11758190	C₂²	1	1	yes	characteristic
27	SD₁₆×Dic₆₁	C₄	1	1	yes	characteristic
28	C₄×#11758201	C₂²	1	1	yes	characteristic
29	#16839849	C₄	1	1	yes	characteristic
30	C₄×#11758200	C₂²	1	1	yes	characteristic
31	#16839847	C₄	1	1	yes	characteristic
32	C₈×D₂₄₄	C₂²	1	1	yes	characteristic
33	D₄×#92418	C₂²	1	1	yes	characteristic
34	#16839827	C₂²	1	1	yes	characteristic
35	C₈×C₂²⋊D₆₁	—	2	1	no	—
36	#16839825	—	2	1	no	—
37	#106×D₆₁	C₄	1	1	yes	characteristic
38	C₄⋊C₈×D₆₁	—	2	1	no	—
39	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₆₁	C₂²	1	1	yes	characteristic
41	#103×D₆₁	C₄	1	1	yes	characteristic
42	#102×D₆₁	C₄	1	1	yes	characteristic
43	C₂²⋊C₈×D₆₁	—	2	1	no	—
44	C₄×C₈×D₆₁	—	2	1	no	—
45	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
48	#16839513	C₂²	1	1	yes	characteristic, complemented
49	#16839512	C₂²	1	1	yes	characteristic, complemented
50	#16839512	C₂²	1	1	yes	characteristic, complemented
51	#16839494	C₂²	1	1	yes	characteristic, complemented
52	Q₈⋊#92418	C₂²	1	1	yes	characteristic, complemented
53	#16839492	C₂²	1	1	yes	characteristic, complemented
54	#16839491	C₂²	1	1	yes	characteristic
55	D₄⋊#92418	C₂²	1	1	yes	characteristic
56	#16839489	C₂²	1	1	yes	characteristic
57	C₈×#92418	C₂²	1	1	yes	characteristic, complemented
58	C₈×#92418	C₂²	1	1	yes	characteristic, complemented
59	C₈×#92418	C₂²	1	1	yes	characteristic, complemented
60	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
61	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
63	C₆₁×#334	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
67	C₂×Q₈×D₆₁	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₆₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₆₁	—	2	1	no	—
70	C₂×#11758190	C₂×C₄	1	1	yes	characteristic
71	C₂×#11758200	C₂×C₄	1	1	yes	characteristic
72	C₂×#11758201	C₂×C₄	1	1	yes	characteristic
73	SD₁₆×D₆₁	C₈	1	8	yes	direct product factor
74	C₂²×#92418	—	2	1	no	—
75	C₂×C₈×D₆₁	—	2	1	no	—
76	C₂×C₈×D₆₁	—	2	1	no	—
77	C₂×C₈×D₆₁	—	2	1	no	—
78	C₂×C₈×D₆₁	—	2	1	no	—
79	C₂×C₈×D₆₁	—	2	1	no	—
80	C₂×C₈×D₆₁	—	4	4	no	—
81	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
84	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
85	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₂₂	—	2	1	no	—
87	C₄×Dic₁₂₂	C₂³	1	1	yes	characteristic
88	#14519742	—	2	1	no	—
89	#14519742	C₂×C₄	1	1	yes	characteristic
90	C₄×D₂₄₄	C₂³	1	1	yes	characteristic
91	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
92	#14519739	C₂×C₄	1	1	yes	characteristic
93	C₄×C₂²⋊D₆₁	—	2	1	no	—
94	#14519737	—	2	1	no	—
95	C₄⋊C₄×D₆₁	—	2	1	no	—
96	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
97	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊C₄×D₆₁	—	2	1	no	—
99	C₄²×D₆₁	—	2	1	no	—
100	C₄²×D₆₁	C₂³	1	1	yes	characteristic
101	#14519709	C₂×C₄	1	1	yes	characteristic
102	#14519708	C₂×C₄	1	1	yes	characteristic
103	#14519708	C₂×C₄	1	1	yes	characteristic
104	C₄⋊#92418	—	2	1	no	—
105	C₄⋊#92418	C₂³	1	1	yes	characteristic
106	C₄⋊#92418	C₂³	1	1	yes	characteristic
107	#14519706	—	2	1	no	—
108	#14519706	—	2	1	no	—
109	#14519706	—	2	1	no	—
110	#14519706	—	2	1	no	—
111	#14519702	C₂×C₄	1	1	yes	characteristic
112	#14519701	C₂×C₄	1	1	yes	characteristic
113	#14519700	C₂×C₄	1	1	yes	characteristic
114	#14519699	C₂×C₄	1	1	yes	characteristic
115	#14519698	C₂×C₄	1	1	yes	characteristic
116	#14519697	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#92418	—	2	1	no	—
118	#14519689	—	2	1	no	—
119	#14519689	—	2	1	no	—
120	C₄×#92418	—	2	1	no	—
121	C₄×#92418	C₂³	1	1	yes	characteristic
122	C₄×#92418	C₂³	1	1	yes	characteristic
123	C₄×#92418	C₂³	1	1	yes	characteristic
124	C₈×Dic₆₁	—	2	1	no	—
125	C₈×Dic₆₁	—	2	1	no	—
126	C₈×Dic₆₁	—	2	1	no	—
127	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₆₁	D₄	1	1	yes	characteristic
130	C₈×Dic₆₁	D₄	1	1	yes	characteristic
131	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
132	C₂²×C₈×C₆₁	—	2	1	no	—
133	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
135	#106×C₆₁	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₆₁	—	2	1	no	—
137	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
139	#103×C₆₁	C₂×C₄	1	1	yes	characteristic
140	#102×C₆₁	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₆₁	—	2	1	no	—
142	C₄×C₈×C₆₁	—	2	1	no	—
143	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
146	C₂³×D₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂×C₂²⋊D₆₁	—	2	1	no	—
151	C₂²×Dic₆₁	—	2	1	no	—
152	Q₈×D₆₁	—	2	2	no	—
153	Q₈×D₆₁	C₂×C₈	1	4	yes	complemented
154	D₄×D₆₁	—	2	2	no	—
155	D₄×D₆₁	C₂×C₈	1	4	yes	—
156	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₆₁	—	2	1	no	—
158	C₂×C₄×D₆₁	—	2	1	no	—
159	C₂×C₄×D₆₁	—	2	1	no	—
160	C₂×C₄×D₆₁	—	2	1	no	—
161	C₂×C₄×D₆₁	—	2	1	no	—
162	C₂×C₄×D₆₁	—	4	2	no	—
163	C₂×C₄×D₆₁	—	4	2	no	—
164	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
167	C₂×Dic₁₂₂	—	2	1	no	—
168	C₂×Dic₁₂₂	C₂²×C₄	1	1	yes	characteristic
169	SD₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	1	no	—
173	C₂×C₈×C₆₁	—	4	2	no	—
174	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
181	C₂²⋊C₄×C₆₁	—	2	1	no	—
182	C₄²×C₆₁	—	2	1	no	—
183	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
184	C₂²⋊Dic₆₁	—	2	1	no	—
185	#11758201	C₂×C₈	1	4	yes	complemented
186	#11758200	C₂×C₈	1	4	yes	complemented
187	#11758198	—	2	1	no	—
188	#11758198	—	2	1	no	—
189	C₄⋊Dic₆₁	—	2	1	no	—
190	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
192	#11758196	—	2	1	no	—
193	#11758196	—	2	1	no	—
194	#11758196	—	2	1	no	—
195	#11758196	—	2	1	no	—
196	C₄×Dic₆₁	—	2	1	no	—
197	C₄×Dic₆₁	—	2	1	no	—
198	C₄×Dic₆₁	—	2	1	no	—
199	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
201	C₄×Dic₆₁	#41	1	1	yes	characteristic
202	C₂×#92418	—	2	1	no	—
203	C₂×#92418	—	2	1	no	—
204	C₂×#92418	—	2	1	no	—
205	C₂×#92418	—	4	2	no	—
206	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
207	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
208	C₂×#92418	C₂×D₄	1	1	yes	characteristic
209	C₂×#92418	C₂×D₄	1	1	yes	characteristic
210	#11758190	C₂×C₈	1	4	yes	complemented
211	C₈×D₆₁	—	2	4	no	—
212	C₈×D₆₁	—	2	2	no	—
213	C₈×D₆₁	—	2	2	no	—
214	C₈×D₆₁	—	4	2	no	—
215	C₈×D₆₁	—	4	2	no	—
216	C₈×D₆₁	—	4	2	no	—
217	C₈×D₆₁	—	4	2	no	—
218	C₈×D₆₁	C₂×C₈	1	4	yes	complemented
219	C₈×D₆₁	SD₁₆	1	4	yes	direct product factor
220	C₂³×C₆₁	—	2	1	no	—
221	C₂²×D₆₁	—	2	1	no	—
222	C₂²×D₆₁	—	2	4	no	—
223	C₂²×D₆₁	—	4	2	no	—
224	C₂²×D₆₁	—	4	2	no	—
225	C₂²×D₆₁	C₄×D₄	1	1	yes	characteristic
226	Q₈×C₆₁	—	2	1	no	—
227	Q₈×C₆₁	C₂²×C₈	1	2	yes	complemented
228	D₄×C₆₁	—	2	1	no	—
229	D₄×C₆₁	C₂²×C₈	1	2	yes	—
230	C₂×C₄×C₆₁	—	2	1	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	1	no	—
235	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
238	C₂²⋊D₆₁	—	2	4	no	—
239	C₂×Dic₆₁	—	2	1	no	—
240	C₂×Dic₆₁	—	2	1	no	—
241	C₂×Dic₆₁	—	2	1	no	—
242	C₂×Dic₆₁	—	4	2	no	—
243	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
244	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
245	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
246	D₂₄₄	—	2	1	no	—
247	D₂₄₄	C₂²×C₈	1	2	yes	—
248	C₄×D₆₁	—	2	4	no	—
249	C₄×D₆₁	—	2	2	no	—
250	C₄×D₆₁	—	4	2	no	—
251	C₄×D₆₁	—	4	2	no	—
252	C₄×D₆₁	—	4	1	no	—
253	C₄×D₆₁	—	4	1	no	—
254	C₄×D₆₁	—	4	2	no	—
255	C₄×D₆₁	C₂²×C₈	1	2	yes	—
256	C₄×D₆₁	#131	1	2	yes	—
257	C₄×D₆₁	C₂×SD₁₆	1	2	yes	—
258	C₄×D₆₁	#135	1	2	yes	—
259	Dic₁₂₂	—	2	1	no	—
260	Dic₁₂₂	—	2	4	no	—
261	Dic₁₂₂	C₂²×C₈	1	2	yes	complemented
262	C₈×C₆₁	—	2	2	no	—
263	C₈×C₆₁	—	2	1	no	—
264	C₈×C₆₁	—	2	1	no	—
265	C₈×C₆₁	—	4	1	no	—
266	C₈×C₆₁	—	4	1	no	—
267	C₈×C₆₁	C₂²×C₈	1	2	yes	complemented
268	C₈×C₆₁	C₂×SD₁₆	1	2	yes	complemented
269	#92418	—	2	2	no	—
270	#92418	—	2	1	no	—
271	#92418	—	2	1	no	—
272	#92418	—	4	1	no	—
273	#92418	—	4	1	no	—
274	#92418	C₂²×C₈	1	2	yes	complemented
275	#92418	C₂×SD₁₆	1	2	yes	complemented
276	C₂×C₈×SD₁₆	—	61	1	no	maximal, Sylow
277	C₂²×C₆₁	—	2	2	no	—
278	C₂²×C₆₁	—	4	1	no	—
279	C₂²×C₆₁	—	4	1	no	—
280	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂×D₆₁	—	2	2	no	—
282	C₂×D₆₁	—	4	1	no	—
283	C₂×D₆₁	—	4	1	no	—
284	C₂×D₆₁	—	4	8	no	—
285	C₂×D₆₁	C₈×D₄	1	2	yes	—
286	C₂×D₆₁	C₄×SD₁₆	1	2	yes	—
287	C₂×D₆₁	#443	1	2	yes	—
288	C₄×C₆₁	—	2	2	no	—
289	C₄×C₆₁	—	2	1	no	—
290	C₄×C₆₁	—	4	1	no	—
291	C₄×C₆₁	—	4	1	no	—
292	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
293	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
294	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
295	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
296	Dic₆₁	—	2	2	no	—
297	Dic₆₁	—	2	1	no	—
298	Dic₆₁	—	4	1	no	—
299	Dic₆₁	—	4	1	no	—
300	Dic₆₁	C₈×D₄	1	2	yes	—
301	Dic₆₁	C₄×SD₁₆	1	2	yes	—
302	C₂×C₈×Q₈	—	61	1	no	—
303	C₂×C₄×SD₁₆	—	61	1	no	—
304	C₂×C₈×D₄	—	61	1	no	—
305	C₈×SD₁₆	—	61	1	no	—
306	C₈×SD₁₆	—	61	1	no	—
307	C₈×SD₁₆	—	61	1	no	—
308	C₈×SD₁₆	—	61	1	no	—
309	C₈×SD₁₆	—	61	1	no	—
310	C₈×SD₁₆	—	61	1	no	—
311	C₈×SD₁₆	—	61	1	no	—
312	C₈×SD₁₆	D₆₁	1	1	yes	characteristic, direct product factor
313	C₂×#334	—	61	1	no	—
314	C₂×Q₈⋊C₈	—	61	1	no	—
315	C₂×D₄⋊C₈	—	61	1	no	—
316	C₂×C₈²	—	61	1	no	—
317	C₂×C₆₁	—	4	2	no	—
318	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
319	C₂×C₆₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
320	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
321	D₆₁	—	4	2	no	—
322	D₆₁	C₈×SD₁₆	1	4	yes	direct product factor
323	C₂²×SD₁₆	—	61	1	no	—
324	C₂³×C₈	—	122	1	no	—
325	C₂×C₄×Q₈	—	61	1	no	—
326	C₂×C₄×D₄	—	61	1	no	—
327	C₈×Q₈	—	61	1	no	—
328	C₈×Q₈	—	61	1	no	—
329	C₈×Q₈	—	61	1	no	—
330	C₈×Q₈	—	122	1	no	—
331	C₈×Q₈	—	122	1	no	—
332	C₈×Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
333	C₄×SD₁₆	—	61	1	no	—
334	C₄×SD₁₆	—	61	1	no	—
335	C₄×SD₁₆	—	61	1	no	—
336	C₄×SD₁₆	—	61	1	no	—
337	C₄×SD₁₆	—	61	1	no	—
338	C₄×SD₁₆	—	61	1	no	—
339	C₄×SD₁₆	—	61	1	no	—
340	C₄×SD₁₆	C₂×D₆₁	1	1	yes	characteristic
341	C₈×D₄	—	61	1	no	—
342	C₈×D₄	—	61	1	no	—
343	C₈×D₄	—	61	1	no	—
344	C₈×D₄	—	122	1	no	—
345	C₈×D₄	—	122	1	no	—
346	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
347	C₂×#106	—	61	1	no	—
348	C₂×C₄⋊C₈	—	61	1	no	—
349	C₂×C₄⋊C₈	—	61	1	no	—
350	C₂×C₄⋊C₈	—	122	1	no	—
351	C₂×#103	—	61	1	no	—
352	C₂×#102	—	61	1	no	—
353	C₂×C₂²⋊C₈	—	122	1	no	—
354	C₂×C₄×C₈	—	61	1	no	—
355	C₂×C₄×C₈	—	61	1	no	—
356	C₂×C₄×C₈	—	61	1	no	—
357	C₂×C₄×C₈	—	122	1	no	—
358	#334	—	61	1	no	—
359	#334	—	61	1	no	—
360	#334	—	61	1	no	—
361	#334	C₂×D₆₁	1	1	yes	characteristic, complemented
362	Q₈⋊C₈	—	61	1	no	—
363	Q₈⋊C₈	—	61	1	no	—
364	Q₈⋊C₈	—	61	1	no	—
365	Q₈⋊C₈	C₂×D₆₁	1	1	yes	characteristic, complemented
366	D₄⋊C₈	—	61	1	no	—
367	D₄⋊C₈	—	61	1	no	—
368	D₄⋊C₈	—	61	1	no	—
369	D₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
370	C₈²	—	61	1	no	—
371	C₈²	—	61	1	no	—
372	C₈²	—	61	1	no	—
373	C₈²	C₂×D₆₁	1	1	yes	characteristic, complemented
374	C₆₁	C₂×C₈×SD₁₆	1	1	yes	characteristic, complemented, Sylow
375	C₂²×Q₈	—	61	1	no	—
376	C₂²×D₄	—	61	1	no	—
377	C₂³×C₄	—	122	1	no	—
378	C₂×SD₁₆	—	61	1	no	—
379	C₂×SD₁₆	—	61	1	no	—
380	C₂×SD₁₆	—	61	8	no	—
381	C₂×SD₁₆	—	61	1	no	—
382	C₂×SD₁₆	C₄×D₆₁	1	1	yes	characteristic
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	61	1	no	—
385	C₂²×C₈	—	61	1	no	—
386	C₂²×C₈	—	61	1	no	—
387	C₂²×C₈	—	61	1	no	—
388	C₂²×C₈	—	122	1	no	—
389	C₂²×C₈	—	122	1	no	—
390	C₂²×C₈	—	122	1	no	—
391	C₂²×C₈	—	122	1	no	—
392	C₂²×C₈	—	122	1	no	—
393	C₂²×C₈	—	122	1	no	—
394	C₂²×C₈	—	244	4	no	—
395	C₄×Q₈	—	61	1	no	—
396	C₄×Q₈	—	61	1	no	—
397	C₄×Q₈	—	61	1	no	—
398	C₄×Q₈	—	122	1	no	—
399	C₄×Q₈	—	122	1	no	—
400	C₄×Q₈	C₂²×D₆₁	1	1	yes	characteristic
401	C₄×D₄	—	61	1	no	—
402	C₄×D₄	—	61	1	no	—
403	C₄×D₄	—	61	1	no	—
404	C₄×D₄	—	122	1	no	—
405	C₄×D₄	—	122	1	no	—
406	C₄×D₄	C₂²×D₆₁	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	61	1	no	—
408	C₂×C₄⋊C₄	—	61	1	no	—
409	C₂×C₄⋊C₄	—	122	1	no	—
410	C₂×C₂²⋊C₄	—	122	1	no	—
411	C₂×C₄²	—	61	1	no	—
412	C₂×C₄²	—	122	1	no	—
413	#106	—	61	1	no	—
414	#106	—	61	1	no	—
415	#106	—	61	1	no	—
416	#106	C₄×D₆₁	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	61	1	no	—
419	C₄⋊C₈	—	61	1	no	—
420	C₄⋊C₈	—	122	1	no	—
421	C₄⋊C₈	—	122	1	no	—
422	C₄⋊C₈	—	122	1	no	—
423	C₄⋊C₈	—	122	1	no	—
424	C₄⋊C₈	—	122	1	no	—
425	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
426	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
427	#103	—	61	1	no	—
428	#103	—	61	1	no	—
429	#103	—	61	1	no	—
430	#103	C₄×D₆₁	1	1	yes	characteristic
431	#102	—	61	1	no	—
432	#102	—	61	1	no	—
433	#102	—	61	1	no	—
434	#102	C₄×D₆₁	1	1	yes	characteristic
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	122	1	no	—
437	C₂²⋊C₈	—	122	1	no	—
438	C₂²⋊C₈	—	122	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	61	1	no	—
441	C₄×C₈	—	61	1	no	—
442	C₄×C₈	—	61	1	no	—
443	C₄×C₈	—	61	1	no	—
444	C₄×C₈	—	61	1	no	—
445	C₄×C₈	—	61	1	no	—
446	C₄×C₈	—	61	1	no	—
447	C₄×C₈	—	122	1	no	—
448	C₄×C₈	—	122	1	no	—
449	C₄×C₈	—	122	1	no	—
450	C₄×C₈	—	122	1	no	—
451	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
452	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
453	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
454	C₂⁴	—	122	1	no	—
455	C₂×Q₈	—	61	4	no	—
456	C₂×Q₈	—	61	1	no	—
457	C₂×Q₈	—	122	1	no	—
458	C₂×Q₈	—	122	2	no	—
459	C₂×Q₈	C₂×C₄×D₆₁	1	1	yes	characteristic
460	C₂×D₄	—	61	4	no	—
461	C₂×D₄	—	61	1	no	—
462	C₂×D₄	—	122	2	no	—
463	C₂×D₄	—	122	1	no	—
464	C₂×D₄	C₂×C₄×D₆₁	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	61	1	no	—
467	C₂²×C₄	—	61	1	no	—
468	C₂²×C₄	—	61	1	no	—
469	C₂²×C₄	—	122	1	no	—
470	C₂²×C₄	—	122	1	no	—
471	C₂²×C₄	—	122	1	no	—
472	C₂²×C₄	—	122	1	no	—
473	C₂²×C₄	—	122	1	no	—
474	C₂²×C₄	—	122	1	no	—
475	C₂²×C₄	—	244	2	no	—
476	C₂²×C₄	—	244	2	no	—
477	SD₁₆	—	61	4	no	—
478	SD₁₆	—	61	4	no	—
479	SD₁₆	—	61	4	no	—
480	SD₁₆	C₈×D₆₁	1	4	yes	direct product factor
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	61	1	no	—
486	C₂×C₈	—	61	1	no	—
487	C₂×C₈	—	61	4	no	—
488	C₂×C₈	—	61	4	no	—
489	C₂×C₈	—	61	1	no	—
490	C₂×C₈	—	61	1	no	—
491	C₂×C₈	—	122	2	no	—
492	C₂×C₈	—	122	2	no	—
493	C₂×C₈	—	122	4	no	—
494	C₂×C₈	—	122	1	no	—
495	C₂×C₈	—	122	1	no	—
496	C₂×C₈	—	122	1	no	—
497	C₂×C₈	—	244	2	no	—
498	C₂×C₈	—	244	2	no	—
499	C₂×C₈	—	244	2	no	—
500	C₂×C₈	—	244	2	no	—
501	C₂×C₈	—	244	2	no	—
502	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
503	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
504	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
505	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	61	1	no	—
508	C₄⋊C₄	—	61	1	no	—
509	C₄⋊C₄	—	122	1	no	—
510	C₄⋊C₄	—	122	1	no	—
511	C₄⋊C₄	—	122	1	no	—
512	C₄⋊C₄	—	122	1	no	—
513	C₄⋊C₄	—	122	1	no	—
514	C₄⋊C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	122	1	no	—
518	C₂²⋊C₄	—	122	1	no	—
519	C₂²⋊C₄	—	122	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	61	1	no	—
522	C₄²	—	61	1	no	—
523	C₄²	—	61	1	no	—
524	C₄²	—	122	1	no	—
525	C₄²	—	122	1	no	—
526	C₄²	—	122	1	no	—
527	C₄²	C₂³×D₆₁	1	1	yes	characteristic
528	C₂³	—	2	1	no	—
529	C₂³	—	61	1	no	—
530	C₂³	—	122	4	no	—
531	C₂³	—	122	1	no	—
532	C₂³	—	244	2	no	—
533	C₂³	—	244	2	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	61	2	no	—
536	Q₈	—	122	4	no	—
537	Q₈	—	122	1	no	—
538	Q₈	C₂×C₈×D₆₁	1	2	yes	complemented
539	D₄	—	2	1	no	—
540	D₄	—	61	2	no	—
541	D₄	—	122	4	no	—
542	D₄	—	122	1	no	—
543	D₄	C₂×C₈×D₆₁	1	2	yes	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	61	1	no	—
550	C₂×C₄	—	61	1	no	—
551	C₂×C₄	—	61	2	no	—
552	C₂×C₄	—	61	2	no	—
553	C₂×C₄	—	61	2	no	—
554	C₂×C₄	—	61	2	no	—
555	C₂×C₄	—	61	1	no	—
556	C₂×C₄	—	122	2	no	—
557	C₂×C₄	—	122	4	no	—
558	C₂×C₄	—	122	1	no	—
559	C₂×C₄	—	122	1	no	—
560	C₂×C₄	—	122	1	no	—
561	C₂×C₄	—	244	2	no	—
562	C₂×C₄	—	244	2	no	—
563	C₂×C₄	—	244	2	no	—
564	C₂×C₄	—	244	2	no	—
565	C₂×C₄	—	244	1	no	—
566	C₂×C₄	—	244	1	no	—
567	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
568	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
569	C₂×C₄	#41×D₆₁	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	61	2	no	—
576	C₈	—	61	2	no	—
577	C₈	—	122	2	no	—
578	C₈	—	122	1	no	—
579	C₈	—	122	1	no	—
580	C₈	—	244	1	no	—
581	C₈	—	244	1	no	—
582	C₈	C₂×C₈×D₆₁	1	2	yes	complemented
583	C₈	SD₁₆×D₆₁	1	2	yes	direct product factor
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	61	2	no	—
588	C₂²	—	61	2	no	—
589	C₂²	—	61	2	no	—
590	C₂²	—	122	2	no	—
591	C₂²	—	244	8	no	—
592	C₂²	—	244	1	no	—
593	C₂²	—	244	1	no	—
594	C₂²	C₄×D₄×D₆₁	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	61	2	no	—
600	C₄	—	61	2	no	—
601	C₄	—	122	1	no	—
602	C₄	—	122	2	no	—
603	C₄	—	244	1	no	—
604	C₄	—	244	1	no	—
605	C₄	C₂²×C₈×D₆₁	1	1	yes	characteristic
606	C₄	#131×D₆₁	1	1	yes	characteristic
607	C₄	C₂×SD₁₆×D₆₁	1	1	yes	characteristic
608	C₄	#135×D₆₁	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	—	61	4	no	—
611	C₂	—	244	2	no	—
612	C₂	C₈×D₄×D₆₁	1	1	yes	characteristic
613	C₂	C₄×SD₁₆×D₆₁	1	1	yes	characteristic
614	C₂	#443×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₆₁
commutator	C₄×C₆₁	C₂³×C₈
Frattini	C₄²	C₂³×D₆₁
Fitting	C₈×SD₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×D₄×D₆₁	C₂×C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₈×SD₁₆	D₆₁
hypocenter	C₆₁	C₂×C₈×SD₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈×Q₈×D₆₁	C₂	semidirect
4. #21444622	C₂	semidirect
5. C₈×#11758190	C₂	semidirect
6. SD₁₆×#92418	C₂	semidirect
7. C₈×#11758201	C₂	semidirect
8. #21444618	C₂	semidirect
9. C₈×#11758200	C₂	semidirect
10. #21444616	C₂	semidirect
11. #334×D₆₁	C₂	semidirect
12. Q₈⋊C₈×D₆₁	C₂	semidirect
14. C₈²×D₆₁	C₂	semidirect
15. C₈×SD₁₆×C₆₁	C₂	semidirect
20. Q₈×#92418	C₂²	semidirect
22. C₈×Dic₁₂₂	C₂²	semidirect
24. #16839886	C₂²	semidirect
48. #16839513	C₂²	semidirect
49. #16839512	C₂²	semidirect
50. #16839512	C₂²	semidirect
51. #16839494	C₂²	semidirect
52. Q₈⋊#92418	C₂²	semidirect
53. #16839492	C₂²	semidirect
57. C₈×#92418	C₂²	semidirect
58. C₈×#92418	C₂²	semidirect
59. C₈×#92418	C₂²	semidirect
60. C₈×Q₈×C₆₁	C₂²	semidirect
63. C₆₁×#334	C₂²	semidirect
64. C₆₁×Q₈⋊C₈	C₂²	semidirect
66. C₈²×C₆₁	C₂²	semidirect
73. SD₁₆×D₆₁	C₈	direct (N × H)
153. Q₈×D₆₁	C₂×C₈	semidirect
169. SD₁₆×C₆₁	C₂×C₈	semidirect
185. #11758201	C₂×C₈	semidirect
186. #11758200	C₂×C₈	semidirect
210. #11758190	C₂×C₈	semidirect
218. C₈×D₆₁	C₂×C₈	semidirect
219. C₈×D₆₁	SD₁₆	direct (N × H)
227. Q₈×C₆₁	C₂²×C₈	semidirect
261. Dic₁₂₂	C₂²×C₈	semidirect
267. C₈×C₆₁	C₂²×C₈	semidirect
268. C₈×C₆₁	C₂×SD₁₆	semidirect
274. #92418	C₂²×C₈	semidirect
275. #92418	C₂×SD₁₆	semidirect
312. C₈×SD₁₆	D₆₁	direct (N × H)
322. D₆₁	C₈×SD₁₆	direct (N × H)
332. C₈×Q₈	C₂×D₆₁	semidirect
361. #334	C₂×D₆₁	semidirect
365. Q₈⋊C₈	C₂×D₆₁	semidirect
373. C₈²	C₂×D₆₁	semidirect
374. C₆₁	C₂×C₈×SD₁₆	semidirect
480. SD₁₆	C₈×D₆₁	direct (N × H)
538. Q₈	C₂×C₈×D₆₁	semidirect
582. C₈	C₂×C₈×D₆₁	semidirect
583. C₈	SD₁₆×D₆₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈×Q₈×D₆₁	2
C₄×SD₁₆×D₆₁	2
C₈×D₄×D₆₁	2
#21444622	2
C₈×#11758190	2
SD₁₆×#92418	2
C₈×#11758201	2
#21444618	2
C₈×#11758200	2
#21444616	2
#334×D₆₁	2
Q₈⋊C₈×D₆₁	2
D₄⋊C₈×D₆₁	2
C₈²×D₆₁	2
C₈×SD₁₆×C₆₁	2
C₂×C₈×SD₁₆	61

Subgroups — C8×SD16×D61 #29649372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×SD₁₆×D₆₁ #29649372